The first quatrain is saying that he envies leaves (I think he's using it in the sense of pages) that his love holds lovingly in her hands -- hands which hold his life (because he loves her so much.

The second quatrain is saying that the lines he writes should be happy because his love will look at them. Even if she's crying for his death, at least the lines should be happy because she's looking at them.

The third quatrain is saying his rhymes should also be happy because she's looking at them. And he's saying that she is his muse -- Mt. Helicon is where the muses were supposed to be from.

The couplet says that all those things should only care about pleasing her because he himself doesn't care about anything else.